Supercritical Nonlinear Schr\"odinger Equations II: Almost Global Existence

Understand

We prove almost global existence for supercritical nonlinear Schr\"odinger equations on the $d$-torus ($d$ arbitrary) on the good geometry selected in part I.

• This is seen as the Cauchy consequence of I, since the known invariant measure of smooth solutions are supported on KAM tori.
• In the high frequency limit, these quantitative solutions could also be relevant to Cauchy problems for compressible Euler equations.